Questions and Answers
Use substitution to solve: 3x-3y=3 and x-5y=-3. What are the values of X and Y?
X=2, Y=1
Find the weighted average of 75, 80, 88, and 93 with weights 1, 2, 3, and 4 respectively.
87.1
Write 2310 as a product of prime factors.
2, 3, 5, 7, 11
Simplify the expression: 1/(X+Y) divided by A/B.
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Use elimination to solve: 2x+2y=14 and 3x-2y=-4. What are the values of X and Y?
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If F(x)=(x)(-x), find F(3).
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Solve the expression: - (1 - 2). What is the result?
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Solve the expression: -2[(-3-2)-2(-2+m)]=-3m-4^2-|-2|. What do you get?
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Solve the expression: (ay + bz) / X1. What is the result with all exponents positive?
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Multiply the expression: (2x-4)(x-3). What is the result?
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Factor the expression: x^2 + 9x + 20. What is the factorized form?
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What do you get when you factor the expression x^2 + x - 30?
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What is the value of (-2)^-2?
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Study Notes
Substitution and Elimination in Systems of Equations
- Substitution method for solving the equations: 3x - 3y = 3 and x - 5y = -3 results in x = 2 and y = 1.
- Elimination method applied to the equations: 2x + 2y = 14 and 3x - 2y = -4 yields x = 2 and y = 5.
Weighted Average Calculation
- Weighted average calculated using scores (75, 80, 88, 93) with weights (1, 2, 3, 4) results in an overall average of 87.1.
Prime Factorization
- Prime factors of 2310 include: 2, 3, 5, 7, and 11.
Simplification of Rational Expressions
- The expression 1/(x+y) divided by A/B simplifies to B/(Ax + Ay).
Function Evaluation
- Evaluating the function F(x) = x(-x) at x = 3 gives F(3) = -9.
Basic Arithmetic Operations
- The solution to -(1 - 2) is -1 + 2, which simplifies to 1.
Solving Complex Equations
- The equation -2[(-3 - 2) - 2(-2 + m)] = -3m - 4^2 - |-2| simplifies to -20/7.
Expression Simplification with Positive Exponents
- The rational expression (ay + bz) / (x^1) simplified with positive exponents results in (ay + bzx) / x.
Polynomial Multiplication
- The product of (2x - 4)(x - 3) expands to 2x² - 10x + 12.
Factoring Quadratic Expressions
- The quadratic x² + 9x + 20 can be factored to (x + 5)(x + 4).
Solving Quadratics
- The equation x² + x - 30 is deemed impossible to factor or solve with real numbers.
Negative Exponents
- The calculation of (-2)^-2 simplifies to 1/4, indicating the reciprocal of the base squared.
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Description
This quiz includes a series of flashcards covering various Algebra 1 concepts such as solving equations using substitution and elimination, calculating weighted averages, and simplifying expressions. Test your skills and knowledge to prepare for your Algebra class!
